Except Q says he killed Martok and Gul Dukat in combat.Picard is at command level.
Physically fighting with super human strength is beneath him.
Command level people just point, and then thousands, if not millions of men just get to it.
It's also a sign of weakness, that he's over compensating for an inferiority complex.
Immortality however is horse of a different colour.
He also killed Sarek, but that sounds like it was an execution not combat.